This article summarizes our present understanding of the physical behavior of two-dimensional turbulent separated flows, which occur due to adverse pressure gradients around streamlined and bluff bodies. The physical behavior of turbulence is flow dependent, so detailed experimental infor­ mation is needed for understanding such flows and modeling their physics for calculation methods. An earlier review (Simpson 1 985) discussed in much detail prior experimental and computational work, and this was followed by an updated review of calculation methods only (Simpson 1 987). Here additional recent references are added to those cited in the two other works. By separation, we mean the entire process of departure or breakaway, or the breakdown of boundary-layer flow. An abrupt thickening of the rotational-flow region next to a wall and significant values of the normal­ to-wall velocity component must accompany breakaway, or otherwise this region would not have any significant interaction with the free-stream flow. This unwanted interaction causes a reduction in the performance of the flow device of interest (e.g. a loss of lift on an airfoil or a loss of pressure rise in a diffuser). It is too narrow a view to use vanishing surface shearing stress or flow reversal as the criterion for separation. Only in steady two-dimensional flow do these conditions usually accompany separation. In unsteady two­ dimensional flow the surface shear stress can change sign with flow reversal without the occurrence of breakaway_ Conversely, the breakdown of the boundary-layer concept can occur before any flow reversal is encountered. In three-dimensional flow the rotational layer can depart without the

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Turbulent Boundary-Layer Separation

Results are presented of an experimental and numerical study of a turbulent boundary layer with pressure gradients conducted using the recent 'fringe method' with its numerical advantages and good inflow quality. After an inflow transient good agreement is observed; the differences, of up to 13 percent, are discussed. Moderate deviations from the law of the wall are found in the velocity profiles of the simulation. They are fully correlated with the pressure gradient, are in fair quantitative agreement with the experimental results of Nagano et al. (1992), and are roughly the opposite of uncorrected mixing-length-model predictions. Large deviations from the wall scaling are observed for other quantities, notably for the turbulence dissipation rate. The a(1) structure parameter drops mildly in the upper layer with adverse pressure gradient.

Experimental and numerical study of a turbulent boundary layer with pressure gradients

A new turbulence closure model designed specifically to treat two-dimensional, turbulent boundary layers with strong adverse pressure gradients and attendant separation is presented The influence of history effects are modelled by using an ordinary differential equation derived from the turbulent kinetic energy equation to describe the stream wise development of the maximum Reynolds shear stress in conjunction with an assumed eddy viscosity distribution that has as its velocity scale the maximum Reynolds shear stress In the outer part of the boundary layer, the eddy viscosity is treated as a free parameter which is adjusted in order to satisfy the ODE for the maximum shear stress Because of this, the model is not simply an eddy viscosity model, but contains features of a Reynolds stress model Comparisons with experiment are presented that clearly show the proposed model to be superior to the Cebeci-Smith one in treating strongly retarded and separated flows In contrast to two-equation, eddy viscosity models, it requires only slightly more computational effort than simple models such as the Cebeci-Smith

A mathematically simple turbulence closure model for attached and separated turbulent boundary layers

The behaviour of a turbulent boundary layer on a flat surface as it encounters the nose of a cylindrical wing mounted normal to that surface is being investigated. A three-component laser anemometer has been developed to measure this highly turbulent three-dimensional flow. Measurements of all the non-zero mean-velocity and Reynolds-stress components have been made with this instrument in the plane of symmetry upstream of the wing. These data have been used to estimate some of the component terms of the turbulence kinetic energy equation. Histograms of velocity fluctuations and short-time cross-correlations between the laser anemometer and a hot-wire probe have also been measured in the plane of symmetry. In all, these results reveal much of the time-dependent and time-averaged turbulence structure of the flow here.Separation occurs in the plane of symmetry because of the adverse pressure gradient imposed by the wing. In the time mean the resulting separated flow consists of two fairly distinct regions: a thin upstream region characterized by low mean backflow velocities and a relatively thick downstream region dominated by the intense recirculation of the mean junction vortex. In the upstream region the turbulence stresses develop in a manner qualitatively similar to those of a two-dimensional boundary layer separating in an adverse pressure gradient. In the vicinity of the junction vortex, though, the turbulence stresses are much greater and reach’ values many times larger than those normally observed in turbulent flows. These large stresses are associated with bimodal (double-peaked) histograms of velocity fluctuations produced by a velocity variation that is bistable. These observations are consistent with large-scale low-frequency unsteadiness of the instantaneous flow structure associated with the junction vortex. This unsteadiness seems to be produced by fluctuations in the momentum and vorticity of fluid from the outer part of the boundary layer which is recirculated as it impinges on the leading edge of the wing. Though we would expect these fluctuations to be produced by coherent structures in the boundary layer, frequencies of the large-scale unsteadiness are substantially lower than the passage frequency of such structures. It therefore seems that only a fraction of the turbulent structures are recirculated in this way.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112090001215

Time-dependent and time-averaged turbulence structure near the nose of a wing-body junction

The experimental results for an equilibrium boundary layer in a strong adverse pressure gradient flow are reported. The measurements show that similarity in the mean flow and the turbulent stresses has been achieved over a substantial streamwise distance where the skin friction coefficient is kept at a low, constant level. Although the Reynolds stress distribution across the layer is entirely different from the flow at zero pressure gradient, the ratios between the different turbulent stress components were found to be similar, showing that the mechanism for distributing the turbulent energy between the different components remains unaffected by the mean flow pressure gradient. Close to the surface the gradient of the mixing length was found to increase from Kl ≈ 0.41 to Kl ≈ 0.78, almost twice as high as for the zero pressure gradient case. Similarity in the triple correlations was also found to be good. The correlations show that there is a considerable diffusion of turbulent energy from the central part of the boundary layer towards the wall. The diffusion mechanism is caused by a second peak in the turbulence production, located at y/δ ≈ 0.45. This production was for the present case almost as strong as the production found near the wall. The energy budget for the turbulent kinetic energy also shows that strong dissipation is not restricted to the wall region, but is significant for most of the layer.

A turbulent equilibrium boundary layer near separation

The problem of turbulent-boundary-layer separation due to an adverse pressure gradient is an old but still important problem in many fluid flow devices. Until recent years little quantitative experimental information was available on the flow structure downstream of separation because of the lack of proper instrumentation. The directionally sensitive laser anemometer provides the ability to measure the instantaneous flow direction and magnitude accurately. The experimental results described here are concerned with a nominally two-dimensional, separating turbulent boundary layer for an airfoil-type flow in which the flow was accelerated and then decelerated until separation. Upstream of separation single and cross-wire hot-wire anemometer measurements are also presented. Measurements in the separated zone with a directionally sensitive laser-anemometer system were obtained for U, V , $\overline{u^2}, \overline{v^2}, - \overline{uv}$ , the fraction of time that the flow moves downstream, and the fraction of time that the flow moves away from the wall. In addition to confirming the earlier conclusions of Simpson, Strickland & Barr (1977) regarding a separating airfoil-type turbulent boundary layer, much new information about the separated region has been gathered. (1) The backflow mean velocity profile scales on the maximum negative mean velocity U N and its distance from the wall N . A U + vs. y + law-of-the-wall velocity profile is not consistent with this result. (2) The turbulent velocities are comparable with the mean velocity in the backflow, although low turbulent shearing stresses are present. (3) Mixing length and eddy viscosity models are physically meaningless in the backflow and have reduced values in the outer region of the separated flow. Downstream of fully developed separation, the mean backflow appears to be divided into three layers: a viscous layer nearest the wall that is dominated by the turbulent flow unsteadiness but with little Reynolds shearing stress effects; a rather flat intermediate layer that seems to act as an overlap region between the viscous wall and outer regions; and the outer backflow region that is really part of the large-scaled outer region flow. The Reynolds shearing stress must be modelled by relating it to the turbulence structure and not to local mean velocity gradients. The mean velocities in the backflow are the results of time averaging the large turbulent fluctuations and are not related to the source of the turbulence.

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The structure of a separating turbulent boundary layer. Part 1. Mean flow and Reynolds stresses

The velocity-probability-distribution flatness and skewness factors for u and v are reported for the separating turbulent boundary layer described by Simpson, Chew & Shivaprasad (1981). Downstream of separation the skewness factor for u is negative near the wall, whereas it is positive upstream of separation. The flatness factor for u downstream of separation differs from the upstream behaviour in that it has a local maximum of about 4 at the minimum mean velocity location in the backflow. Both upstream and downstream of separation the skewness factor for v has a profile shape and magnitudes that are approximately the mirror image or negative of the skewness factor for u. The flatness factor for v seems to be affected little by separation.Examination of the momentum and turbulence-energy equations reveals that the effects of normal stresses are important in a separating boundary layer. Negligible turbulence-energy production occurs in the backflow. Turbulence-energy diffusion is increasingly significant as separation is approached and is the mechanism for supplying turbulence energy to the backflow.The backflow appears to be controlled by the large-scale eddies in the outer region flow, which provides the mechanism for turbulence-energy diffusion. The backflow behaviour does not appear to be significantly dependent on the far downstream near-wall conditions when the thickness of the backflow region is small compared with the turbulent shear layer thickness.

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The structure of a separating turbulent boundary layer. Part 2. Higher-order turbulence results

Simpson, Chew & Shivaprasad (1981 a , b) describe many experimentally determined features of a separating turbulent boundary layer. For the same flow, experimental results for the transverse velocity component are presented here. A specially designed directionally sensitive laser anemometer was constructed and used to make measurements in the separated region. Cross-wire hot-wire anemometer measurements were obtained upstream of separation and in the outer region of the separated flow and are in good agreement with the laser anemometer results. It was found that wI2 = v t2 in the outer 90 yo of the shear layer both upstream and downstream of separation. Features of wI2 profiles in the backflow are related to features of the streamwise velocity component. This behaviour is consistent with the large-scale-structures flow model of a separating boundary layer presented by Simpson et al. (1981a, b ) . Large-scale structures supply the mean streamwise backflow. These large-scale structures also transport the turbulence energy to the backflow from the outer flow by turbulent diffusion since advection and production of turbulence kinetic energy are negligible there compared with the dissipation rate. Because of continuity requirements fluid motions toward the wall must be deflected and contribute to streamwise and transverse motions near the wall.

http://www.dept.aoe.vt.edu/~simpson/aoe6154/ShilohShivSimp%20Separated%20Flow%20JFM%20Part3%201981.pdf

The structure of a separating turbulent boundary layer. Part 3. Transverse velocity measurements

Measurements were obtained of the sinusoidal unsteadiness of the free stream velocity during the separation of the turbulent boundary layer. Data were gathered by single wire and cross-wire, anemometry upstream of flow detachment, by laser Doppler velocimetry to detect the movement of the flow in small increments, and by a laser anemometer in the detached zone to measure turbulence and velocities. The study was restricted to a sinusoidal instability frequency of 0.61 and a ratio of oscillation amplitude to mean velocity of 0.3. Large amplitude and phase variations were found after the detachment, with unsteady effects producing hysteresis in the relationships between flow parameters. The detached shear layer decreased in thickness with increasing free-stream velocity and increases in the Reynolds shear stress. Deceleration of the free stream velocity caused thickening in the shear layer and upstream movement of the flow reversal location. The results are useful for studies of compressor blade and helicopter rotors in transition.

http://www.dept.aoe.vt.edu/~simpson/aoe6154/SimpShivaChew%20Unsteady%20Sep%20JFM%20Part%204%201983.pdf

The structure of a separating turbulent boundary layer. Part 4. Effects of periodic free-stream unsteadiness

The results of experimental trials to obtain measurements of the effects of frequency on the sinusoidal variations in the free stream velocity over a separating turbulent boundary layer are reported. An oscillation frequency of 0.596 Hz was examined, in conjunction with a free stream velocity of 10.18 m/sec. Hot-wire anemometers measured the velocity upstream of the separation and the phase-averaged skin friction, while the velocities in the detached flow zone and the downstream velocity were assayed with a laser anemometer. Large amplitude and phase variations developed at the beginning of separation, producing hysteresis in the relationships between flow parameters. Increases in the free stream velocity decreased the detached shear layer thickness, while in the deceleration segment of the cycle the separated shear layer grew thicker. The results are in a frequency range that are significant for axial compressor blades and helicopter blades.

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B. G. Shivaprasad

Papers

The structure of a separating turbulent boundary layer. Part 1. Mean flow and Reynolds stresses

The structure of a separating turbulent boundary layer. Part 2. Higher-order turbulence results

The structure of a separating turbulent boundary layer. Part 3. Transverse velocity measurements

The structure of a separating turbulent boundary layer. Part 4. Effects of periodic free-stream unsteadiness

The structure of a separating turbulent boundary layer. V Frequency effects on periodic unsteady free-stream flows